Limit State Design Concept V.N.Kundlikar Visit for more Learning Resources

INTRODUCTION Designer has to ensure the structures, he designs are: Fit for their purpose Safe Economical and durable

Uncertainties affecting the safety of a structure are due to: INTRODUCTION-2 Uncertainties affecting the safety of a structure are due to: uncertainty about loading uncertainty about material strength and uncertainty about structural dimensions and behaviour

Statistical Meaning of Safety INTRODUCTION-3 Frequency Curve (a) Risk of failure Variation of resistance (R.M.) between nominally identical materials Load used in calculation Strength (or resistance) used in calculations Curve (b) Variation of maximum life time load effects (B.M.) Statistical Meaning of Safety Load effects divided by Resistance moment

Uncertainties in service life are due to: INTRODUCTION - 4 Uncertainties in service life are due to: Variability of the loads Variability of the load distribution through the structure Characteristic resistance: Value of resistance below which not more than a prescribed percentage of test results may be expected to fall Characteristic load: Value of the load, which has an accepted probability of not being exceeded during the life span of the structure.

Actions Permanent Actions Qp Variable Actions Qv Accidental Actions Qa

Characteristic Actions Qc Are those values of different actions that are not expected to be exceeded with more than 5 % probability during the life of the structure

Design Action Qd Qd = ∑ fk Qck k

Design Strength Sd Sd = Su / m

ALLOWABLE STRESS DESIGN (ASD) Stresses caused by the characteristic loads must be less than an “allowable stress”, which is a fraction of the yield stress. Allowable stress may be defined in terms of a “factor of safety" which represents a margin for overload and other unknown factors which could be tolerated by the structure.

Limitations Allowable stress = (Yield stress) / (Factor of safety) ALLOWABLE SRESS DESIGN (ASD) - 2 Allowable stress = (Yield stress) / (Factor of safety) Limitations material non-linearity non-linear behaviour in the post buckled state and the property of steel to tolerate high stresses by yielding locally and redistributing the loads not accounted for. no allowance for redistribution of loads in statically indeterminate members

A typical example of a set of load combinations is given below, which accounts for the fact that the dead load, live load and wind load are all unlikely to act on the structure simultaneously at their maximum values: (Stress due to dead load + live load) < allowable stress (Stress due to dead load + wind load) < allowable stress (Stress due to dead load + live load + wind) < 1.33 times allowable stress.

Summary of WSD In practice there are severe limitations to this approach. These are the consequences of material non-linearity, non-linear behaviour of elements in the post-buckled state and the ability of the steel components to tolerate high theoretical elastic stresses by yielding locally and redistributing the loads. Moreover the elastic theory does not readily allow for redistribution of loads from one member to another in a statically indeterminate structures.

LIMIT STATE DESIGN “Limit States" are the various conditions in which a structure would be considered to have failed to fulfil the purpose for which it was built. “Ultimate Limit States” are those catastrophic states,which require a larger reliability in order to reduce the probability of its occurrence to a very low level. “Serviceability Limit State" refers to the limits on acceptable performance of the structure.

General Principles of Limit State Design Structure to be designed for the Limit States at which they would become unfit for their intended purpose by choosing, appropriate partial safety factors, based on probabilistic methods. Two partial safety factors, one applied to loading (f) and another to the material strength (m) shall be employed.

f allows for; the possible deviation of the actual behaviour of the structure from the analysis model deviation of loads from specified values and reduced probability that the various loads acting together will simultaneously reach the characteristic value.

m takes account; the possible deviation of the material in the structure from that assumed in design the possible reduction in the strength of the material from its characteristic value and manufacturing tolerances. Mode of failure (ductile or brittle).

Table 1: Limit States Limit State of Strength Serviceability Limit State Strength (yield, buckling) Stability against overturning and sway Fracture due to fatigue Brittle Fracture Deflection Vibration Repairable damage due to fatigue Corrosion Fire Table 1: Limit States

S* - factored load effect PARTIAL SAFETY FACTOR S*  R* S* - factored load effect R*- factored resistance of the element being checked, and is a function of the nominal value of the material yield strength.

Limit State of Strength Limit state of Serviceability Partial Safety Factor for Loads Combination Limit State of Strength Limit state of Serviceability DL LL’ WL/ EL AL DL LL’ WL/EL Leading Accompanying Leading Accompanying DL+LL+CL 1.5 1.5 1.05   1.0 1.0 1.0  DL+LL+CL+ WL/EL 1.2 1.2 1.05 0.53 0.6 1.2  1.0 0.8 0.8 0.8 DL+WL/EL 1.5 (0.9)*   1.5  1.0   1.0 DL+ER 1.2 (0.9) 1.2        0.35 DL+LL+AL 1.0 0.35  1.0     * This value is to be considered when the dead load contributes to stability against overturning is critical or the dead load causes reduction in stress due to other loads. ‘ When action of different live loads is simultaneously considered, the leading live load is whichever one causes the higher load effects in the member/section. Abbreviations: DL= Dead Load, LL= Imposed Load (Live Loads), WL= Wind Load, CL= Crane Load (Vertical/horizontal), AL=Accidental Load, ER= Erection Load, EL= Earthquake Load.

Resistance of connection m1 Partial Safety Factor for Material Sl. No. Definition Partial Safety Factor 1 Resistance, governed by yielding m0 1.10 2 Resistance of member to buckling m0 3 Resistance, governed by ultimate stress m1 1.25 4 Resistance of connection m1   (i) Bolts-Friction Type, mf (ii) Bolts-Bearing Type, mb (iii)  Rivets, gmr (iv)  Welds, gmw Shop Fabrications Field Fabrications 1.50

LIMIT STATES FOR DESIGN PURPOSES Ultimate Limit State is related to the maximum design load capacity under extreme conditions. The partial load factors are chosen to reflect the probability of extreme conditions, when loads act alone or in combination. Serviceability Limit State is related to the criteria governing normal use. Unfactored loads are used to check the adequacy of the structure. Fatigue Limit State is important where distress to the structure by repeated loading is a possibility.

Limit State of serviceability Type of Building Deflection Design Load Member Supporting Maximum Deflection Industrial building Vertical Live load/Wind load Purlins and Girts Elastic cladding Brittle cladding Span / 150 Span / 180 Live load Simple span Span / 240 Span / 300 Cantilever span Span / 120 Live load or Wind load Rafter supporting Profiled Metal Sheeting Plastered Sheeting Crane load (Manual operation) Gantry Crane Span / 500 (Electric operation up to 50 t) Span / 750 (Electric operation over 50 t) Span / 1000 Lateral No cranes Column Height / 150 Masonry/Brittle cladding Height / 240 Crane + wind Gantry (lateral) Crane(absolute) Span / 400 Relative displacement between rails 10 mm Crane+ wind Column/frame Gantry (Elastic cladding; pendent operated) Height / 200   Gantry (Brittle cladding; cab operated) Height / 400

Cantilever Other Buildings Vertical Live load Floor & Roof Elements not susceptible to cracking Span / 300 Elements susceptible to cracking Span / 360 Cantilever Span / 150 Span / 180 Lateral Wind Building Elastic cladding Height / 300 Height / 500 Brittle cladding Inter storey drift --- Storey height / 300

TOPICS COVERED AND CONCLUSIONS Review of the provisions of safety, consequent on uncertainties in loading and material properties. Allowable Stress Design Limit State Design

For more detail contact us THANK YOU For more detail contact us